Compression stiffness of circular bearings of laminated elastic material interleaving with flexible reinforcements

The compression stiffness of a circular bearing that consists of laminated elastic layers interleaving with flexible reinforcements is derived in closed form. The effect of bulk compressibility in the elastic layer and the effect of boundary condition at the ends of the bearing are considered. The stiffness of the bearing with monotonic deformation is derived first. Then, the bearings with both ends being free from shear force and the bearings with both ends being bonded to rigid plates are studied. The theoretical solutions to the compression stiffness of the bearings are extremely close to the results obtained by the finite element method, which proves that the displacement assumptions utilized in the theoretical derivation are reasonable.     

Buckling load of seismic isolators affected by flexibility of reinforcement

Using the thinner steel reinforcing plates in the elastomeric multilayer isolators could reduce the weight of the isolators but would have a large effect on the buckling load of an isolator, which cannot be analyzed by the Haringx theory, a traditional approach on the stability analysis of rubber bearings. The buckling load of the isolators, which includes the effect of the flexibility of the steel reinforcing plates, is analyzed by a beam theory in which shear deformation and warping of the cross-section are considered. Pressure distributions in the elastomeric layer bonded to flexible reinforcements under compression force, bending moment and warping moment are derived from an assumed displacement field, from which the warping-related parameters used in the beam theory are established. The thickness of the steel reinforcement in the isolators is determined from the buckling load of the isolators, which is solved from a cubic equation established by the beam theory.     

Compression stiffness of infinite-strip bearings of laminated elastic material interleaving with flexible reinforcements

The closed-form solutions to the compression stiffness of the laminated elastomeric bearings of infinite-strip shape with flexible reinforcements are derived. The effect of bulk compressibility in the elastic layer and the effect of boundary condition at the ends of the bearing are considered. Three types of the elastic layers bonded to flexible reinforcements are studied. The first type simulates the interior elastic layers of the bearings with shear-free ends. The second type simulates the exterior elastic layers of the free-end bearings. The third type simulates the elastic layers in the bearings which ends are bonded to rigid plates. The theoretical solutions to the compression stiffness of the bearings are extremely close to the results obtained by the finite element method, which proves that the displacement assumptions utilized in the theoretical derivation are reasonable.     

Tilting analysis of circular elastic layers interleaving with flexible reinforcements

Bonding with reinforcements can increase the stiffness of elastic layers in the normal direction. The flexibility effect of the reinforcement on the bonded elastic layers of a circular cross-section subjected to pure bending moment is analyzed through a theoretical approach. Based on two kinematics assumptions in the elastic layers, the closed-form solutions of the horizontal displacements in the elastic layers and the reinforcements are solved using the governing equations established by stress equilibrium in the elastic layers and the reinforcements. Through these solved displacements, the tilting stiffness of the bonded elastic layer, the shear stress on the bonding surfaces, and the internal forces of the reinforcements are derived in closed forms.     

非加劲钢板剪力墙的高阶弹性剪切屈曲分析

非加劲钢板剪力墙(SPSW)结构在水平荷载作用下易屈曲,形成主拉压应力场,并以拉力带方式提供水平承载力及抗侧刚度。传统拉杆模型(SM模型)用于非加劲SPSW结构分析或设计时忽略压力场的贡献,一般会低估高厚比较小的非加劲SPSW结构的抗侧能力。非加劲SPSW结构在水平力作用下会形成多波面外变形,与剪力墙板的高阶屈曲相似,可通过在修正的SM模型中引入对应于高阶屈曲的主压应力来反映压力场贡献,提高模型分析精度。考虑剪力墙板高厚比、高宽比及边缘构件刚度的影响,共设计66个单层、单跨和梁柱铰接的非加劲SPSW算例,并进行弹性屈曲分析。分析结果表明,高厚比及边缘构件刚度对非加劲SPSW结构的剪切屈曲系数影响不大;随着剪力墙板高宽比的增加,非加劲SPSW结构的剪切屈曲系数呈增大趋势。采用Matlab程序对66个非加劲SPSW算例的2～5阶剪切屈曲系数结果进行统计分析,并提出了简化公式。     

钢-混凝土组合梁负弯矩区畸变屈曲弯矩计算公式

侧向弯曲屈曲及侧向弯扭屈曲均为钢-混凝土组合梁负弯矩区钢梁的重要屈曲模式,而现有计算方法通常只考虑到侧向弯曲屈曲,未考虑到侧向弯扭屈曲,因此有一定局限性。本文在钢梁腹板对钢梁下翼缘的转动约束刚度及侧向约束刚度的计算公式上,结合弹性介质中薄壁杆件的屈曲理论推导了工形钢-混凝土组合梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算公式。实例分析表明,现有计算方法均存在一定理论缺陷,本文计算方法更为合理;同时,本文计算式比现有文献中同类型计算式更为简洁,便于手算,实用性强并适于工程应用。     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

Buckling of short beams with warping effect included

A beam theory for the stability analysis of short beam that includes shear deformation and warping of the cross-section is developed. The warping of the cross-section is taken to be an independent kinematics quantity and corresponding force resultants are defined. For the beam subjected to the external loading only at the ends of the beam, equilibrium equations have been obtained by the principle of virtual work. The variations of lateral displacement, rotational angle of the cross-section and the multiplier of the warping shape along the beam axis are solved in closed form and expressed in terms of deformation quantities at the ends of the beam. Based on this beam theory, the lateral stiffness of the beam sustained an axial compression force and a lateral shear force at one end is explicitly derived, from which the equation of the buckling load is established and the buckling load can be solved. When the effect of cross-section warping is neglected, the derived lateral stiffness and buckling load converge to the solutions of the Haringx theory.     

Analysis of microbuckling for monomolecular layers adhering to a substrate

A two-dimensional linear spring model is established to study the microbuckling of a plane monomolecular layer adhering to a substrate. The model is for the layer subjected to a compressive load having an arbitrary angle with the chemical bond of the layer. The effects of the load angle, the strength of adhesion and the bending stiffness and shearing stiffness (the capability of resisting transverse bending and in-plane shearing) of the layer on the minimal buckling force and the critical buckling mode are discussed. It is found that the minimal buckling force increases with increasing load angle and, for a given bending stiffness, increases with increasing strength of adhesion and decreasing shearing stiffness. Furthermore, a critical condition under which the buckling of the layer can just occur is obtained, which is helpful to avoid buckling in an engineering application. The project supported by the National Distinguished Young Scientist Fund, Cheung Kong Scholars Programme, the National Natural Science Foundation of China (10272082, 10172068) and Shanghai Postdoctoral Science Foundation     

Experimental and theoretical study of the buckling of narrow thin plates on an elastic foundation under compression

The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate–substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation.     

带接头在役混凝土电杆受力性能试验研究

为了揭示在役混凝土电杆连接接头的破坏机理和承载性能,进行了6根两类不同杆长、跨中带钢圈接头的混凝土电杆的抗弯承载力试验,通过试验观察了各试件的受力全过程和破坏形态,获取了弯矩-挠度曲线、裂缝宽度-弯矩曲线、刚度退化规律曲线以及极限弯矩等重要指标.对比分析了两种杆长试件的承载力和刚度变化规律,并通过试验拟合,提出了相关刚度退化规律公式.研究结果表明,试件所具有的破坏形态大多为混凝土拉裂、接头钢圈不屈服,破坏具有明显的脆性;截面的平均应变符合平截面假定;杆长较短试件的极限承载力显著大于较长杆长的试件;裂缝宽度-弯矩曲线大致经历了4个阶段:即未开裂阶段、逐渐增长阶段、稳定发展阶段、快速开裂阶段;杆长较短试件的初始弹性刚度以及弹塑性刚度都比较长杆长试件的大;电杆连接接头的相对刚域范围对杆身受力性能具有极大的影响.     

反倾层状岩体斜坡弯曲-拉裂两种失稳破坏之判据探讨

对反倾层状岩体斜坡弯曲-拉裂的失稳破坏判据,已有研究分别基于两种力学模型进行推导,即竖直压杆弹性屈曲稳定和平直梁弯折破坏模型,但对层间错动阻力及挠度产生附加弯矩等因素未加以考虑,不尽合理。在反倾斜坡岩层受力分析基础上,建立考虑了板侧层间错动阻力的下端嵌固、上端自由的斜置等厚弹性悬臂板梁模型,统一地通过瑞利-里兹能量方法,推导了弹性屈曲临界条件和嵌固端弯折破坏临界条件。实例计算及讨论表明,弹性屈曲判据适用于陡立岩层;而中-陡反倾岩层应主要为弯折破坏,但层间的力学性质对弯折临界判据值具有较大影响。     

弹性地基双层梁理论下的混凝土路面力学分析

为建立混凝土路面结构受力分析计算模型,以Winkler弹性地基梁模型为基础,推导出了弹性地基双层梁理论的表达式;给定边界条件,利用MATLAB软件获得了无限长弹性地基梁在集中力作用下的挠度表达式。将混凝土路面结构简化为弹性地基上的双层梁,当车辆荷载作用于混凝土路面时,在集中载荷的作用下,建立了面层与基层的微分平衡方程。应用广义“初参数”法,得到了双层梁位移和应力的解析解。通过算例,对面层及基层的变形和应力进行了分析,结果表明:增大面层、基层的轴惯性矩和地基的弹性常数,可以有效地减少面层和基层的变形量,降低最大应力数值,但抗弯刚度对基层和面层的弯矩受力影响不大。最后将结果与ANSYS分析结果进行了比较,佐证了解的可靠性,研究结果可为混凝土路面结构设计提供依据。     

Analytical springback model for lightweight hexagonal close-packed sheet metal

Experiments have shown that magnesium alloy sheet a common hexagonal close-packed metal, exhibits mechanical behavior unlike that of sheets made of cubic metals (X.Y. Lou et al., 2007, Int. J. Plasticity, 24, 44). The unique stress–strain response includes a strong asymmetry in the initial yield and subsequent plastic hardening. In other words, the stress–strain curves in tension and compression are significantly different. A proper representation of the constitutive relationships is crucial for the accurate evaluation of springback, which occurs due to the residual moment distribution through the sheet thickness after bending. In this paper, we propose an analytical model for asymmetric elasto-plastic bending under tension followed by elastic unloading in order to evaluate the bending moment, which is equivalent to the springback amount. To simplify the calculations, the experimentally measured stress–strain curve of the magnesium alloy sheet was approximated with discrete linear hardening in each deformation region, and the material properties were characterized according to several simplifying assumptions. The bending moment was calculated analytically using the approximate asymmetric stress–strain relationship up to the prescribed curvature corresponding to the radius of the tool in sheet metal forming operations. A numerical example showed an unusual springback increase, even with an increase in the applied force; this is an unexpected result for conventional symmetric materials. We also compared the calculated springback amounts with the results of physical measurements. This showed that the proposed model predicts the main trends of the springback in magnesium alloy sheets reasonably well considering the simplicity of the analytical approach.     

Static and dynamic behavior of disk bearings for OSPG railway bridges under railway vehicle loading

The aim of the present study is to investigate the static and dynamic behavior of disk bearings under railway vehicle loadings. A disk bearing is operated as an elastic bearing in the vertical direction and is composed of a Polyether Urethane (Polyurethane) disk for elastic support and Polytetrafluoroethylene (PTFE) to accommodate lateral movements. Static tests are conducted in a laboratory to determine the static behavior of a Polyurethane disk. Finite Element (FE) analysis is also performed to assess the friction and the role of the pin inside a disk bearing. For dynamic behavior, four disk bearings having the identical Polyurethane disk, which are used in the static tests, are installed in a real railway bridge and tested under a running locomotive. From the test results, the static and dynamic stiffness of disk bearings are estimated and compared with each other. The estimated static stiffness of the disk bearing is almost half of that under dynamic loading. In addition, under relatively light loads the dynamic stiffness of a fixed disk bearing is approximately 80% greater than that of an expansion disk bearing since the PTFE deflects and the gap is closed in the expansion bearing. Deformation of the disk bearings in the real bridge is measured with varying locomotive speeds. The deformation of the disk bearings does not vary significantly with changes in the locomotive’s speed.     

THE TRANSVERSE NONLINEAR FREE VIBRATION AND THE BUCKLING OF A COMPRESSIVE BAR ON AN ELASTIC FOUNDATION

基于Hamilton 原理,运用假设时间模态法,得到了弹性基础上压杆的横向非线性自由振动与屈曲的位移型常微分控制方程. 考虑一端固定另一端可移简支边界条件,采用打靶法得到了结构第一至第三阶结构频率与一阶屈曲载荷的数值结果. 结果表明：随轴心压力增加,结构频率减小;随弹性基础刚度增加,结构频率与屈曲载荷均增加;弹性基础刚度对结构频率的影响随振型阶数增加在减小;在小振幅的情形下,不同振型对一阶屈曲载荷的影响很小.     

Thermal buckling and post-buckling response of imperfect temperature-dependent sandwich FGM plates resting on elastic foundation

Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients.     

外套有/无约束条件下波纹管扭转特性的实验研究

波纹管是一种具有极高扭转刚度，但易于失稳的弹性薄壁壳体。由于波纹管通常在很小的扭转角度下就会发生失稳，限制了其在传递扭矩方面的用途。通过实验研究发现，波纹管扭转屈曲时其材料远未到达强度极限，使得材料的利用率较低。波纹管失稳以后依然可以在一定范围内承受增大的扭矩，其在弹性范围内的扭转角度远大于屈曲发生时的扭转角度。为提高波纹管在后屈曲阶段的承载能力，采用具有合适内径的刚性外套来约束其横向弯曲变形。通过实验研究与有限元分析相结合的方法，比较了后屈曲阶段外套在提高波纹管承载能力方面的作用，两者得到了一致的结论，外套约束对波纹管后屈曲阶段的承载增加作用明显。     

ON THE ORIENTATION OF BUCKLING DIRECTION OF ANISOTROPIC ELASTIC PLATE UNDER UNIAXIAL COMPRESSION

The theory of small deformation superimposed on a large deformation of an elastic solid is used to investigate the buckling of anisotropic elastic plate under uniaxial compression. The buckling direction (the direction of buckling wave) is generally not aligned with the compression direction. The equation for determining the buckling direction is obtained. It is found that the out-of-plane buckling of anisotropic elastic plate is possible and both buckling conditions for flexural and extensional modes are presented. As a specific case of buckling of anisotropic elastic plate, the buckling of an orthotropic elastic plate subjected to a compression in a direction that forms an arbitrary angle with an elastic principal axis of the materials is analyzed. It is found that the buckling direction depends on the angle between the compression direction and the principal axis of the materials, the critical compressive force and plate-thickness parameters. In the case that the compression direction is aligned with the principal axis of the materials, the buckling direction will be aligned with the compression one irrespective of critical compressive force and plate-thickness. Project supported by the National Natural Science Foundation of China (No. 19772032).     

Nondestructive shell-stability estimation by a combined-loading technique

Accurate nondestructive procedures for cylindrical-shell-stability investigations have long been a goal of experimentalists and practicing engineers. Stability criteria based on stress and deflection have been investigated intensively by researchers, but lateral-stiffness variation has been largely ignored. It is this aspect which is the foundation of the present work. The variation of specimen lateral stiffness with compressive axial loading is studied experimentally and it is demonstrated that buckling loads can be predicted for monocoque shells from such data. A study of the initial specimen geometry is presented and an evaluation is made of its effect on the distribution of stiffness at zero axial load. When the lateral test force used to termine the stiffness is considered as a destabilizing load in combination with the axial compression, it is shown that critical values of the force can be estimated by the “Southwell plat” procedure. These critical forces can be correlated with axial load and extrapolated to yield an accurate estimate of the buckling load. The approach greatly reduces the compressive load necessary for stability predictions over that required for other techniques.